Monday, May 18, 2009
I'm an optimist when it comes to TV viewing. I record dozens of shows with the very real intent of watching them all, then spend fifteen minutes once a week deleting most of them. If people ask me if I've seen a program I cheerfully answer "No, but I recorded it!" Every once in a while I have the opportunity to actually see one of the shows I recorded, generally because I'm shirking some other responsibility like laundry or writing. Earlier this week I watched an episode of "Numb3rs" about an FBI agent and his genius math brother who solves crimes using brute force and clever number theory. It's a slight drama, but entertaining. During this particular episode there was a crawl across the screen with the teaser, "Test your own math skills by trying the puzzles at CBS.com." I jumped at the opportunity to validate my intelligence (or scoff at the ridiculousness of the questions if I couldn't solve them). This week's puzzle concerned convergence using lines that bisected triangle sides and angles. While I enjoyed the questions, they led me to further consideration about convergence as it relates to soccer. Yes, I'm that obsessed with soccer!
Convergence in math means the same thing it does in English – a coming together from different directions at a single point (Encarta Dictionary). Soccer succeeds or fails because of convergence or the lack thereof. Yesterday, Robbie's team had a state championship play-off game that frustratingly demonstrated the elements of convergence. I should mention that convergence is either exhilarating or frustrating when it comes to soccer. Yesterday an opponent's foot converged twice with one of Robbie's teammate's faces. The second convergence resulted in thirteen stitches. The lightning and deluge converged with twilight to require an early game termination. The uneven new sod patches converged with an errant kick to insure an erratic bounce into the goal. Players regularly converged for fouls or tackles or steals. We finally had an exhilarating convergence when a ball was struck from the corner by one forward while the other charged in, met it at the goal line and converged it right into the back of the net.
When you relate soccer anecdotes they usually involve convergence. So while you may not have stayed awake during your Geometry class, you still use the mathematical precepts to make your point. "I thought the ball was going in, but the keeper just managed to deflect it." "That defender came out of nowhere to steal the ball right off of my daughter's foot." "The ball caromed off the post and into the goal." "That dad got right in the official's face." Players converge at the end of the game in the traditional handshake. We even use convergence to get to the games when we set our GPS and it charts a course for us. It's creating a convergence between the spot we need to be and the route our vehicle travels even if it isn't a straight bisector.
My other favorite sport is baseball. I'm happy to spend a few hours at the ballpark absorbing the sights and sounds of a Brewers game. On the face of it, baseball and soccer couldn't be more different in their production. Baseball is a game of fits and starts, especially in the eighth inning of a close game where pitching changes can make that one inning last nearly as long as the rest of the game. Players in the outfield might go long minutes before even moving, much less chasing a ball. But when they are needed, they are needed in a spectacular hurry. Soccer is nearly non-stop, everyone is needed all the time, and players have to be constantly on the move, readjusting their position depending upon the direction and speed of play. But I realized that what I love about baseball I also love about soccer. Both games require mathematical precision which is based on convergence.
That's why I don't like watching baseball on TV, because the camera dictates where I look. I want to survey the field, see where the outfielders are shifting, judge the wind, watch runners lead off, and get a good feel for the ball's direction both when hit and when thrown. Players make judgments about their position based on the angle they expect the ball to travel. In other words, they place themselves in the mostly likely spot for convergence or near enough to a range of convergence points. There are some intuitive calculations concerning trajectories, resistance, and velocity that dictate the point of convergence and the likelihood of success. Pitchers, hitters, infielders, outfielders, and coaches are all doing their own math in their heads to determine what will create the best outcome. Pitchers want to have their pitches converge with the catcher's mitt, hitters want their bats to converge with the ball, and fielders want their mitts to converge with any hit. Likewise a soccer player makes a decision about using left or right foot, inside or outside, force of the kick, and obstacles to pick the most likely point of convergence with the ball that will alter its route right into the goal or to another teammate's foot. These players do this all within a blink of the eye and they do it hundreds of times in a game. Even more amazingly, unlike math students who can do their calculations in relative calm and without immediate criticism, players resolve their mathematical equations in an instant with on the spot evaluations given at the top of someone's lungs. There's no time to recalculate, check the variables, ponder the choices. It's now or never and then on to the next problem.
While I don't advocate protractors and graphic calculators as part of an essential soccer kit, I do recognize the beauty of math in what is happening on the field. The next time you watch a ball leave a player's foot and land perfectly in front of another player, or see a player suddenly step in front of an opponent to triumphantly settle a goal kick, or witness that awesome bend it like Beckham moment, give pause to consider Euclid, Aristotle, and Pythagoras. Sure, these ancient Greeks didn't invent soccer, but their geometrical explorations resulted in tools for analyzing and improving soccer play. With their acute understanding of convergence, they probably would have made fantastic coaches. Maybe they were. "Go Polyhedrons!"